2003 AMC 12A Problems/Problem 19
A parabola with equation is reflected about the -axis. The parabola and its reflection are translated horizontally five units in opposite directions to become the graphs of and , respectively. Which of the following describes the graph of ?
If we take the parabola and reflect it over the x - axis, we have the parabola . Without loss of generality, let us say that the parabola is translated 5 units to the left, and the reflection to the right. Then:
Adding them up produces:
\[(f + g)(x) &= ax^2 + (10a+b)x + 25a + 5b + c - ax^2 + 10ax -bx - 25a + 5b - c &= 20ax + 10b\] (Error compiling LaTeX. ! Misplaced alignment tab character &.)
This is a line with slope . Since cannot be (because would be a line) we end up with